These are the bonus unlockables for Max Payne 3. You need to complete the second part to unlock the specific bonus indicated in the first part.

Character Select option in Arcade mode: Successfully complete the game on the Medium difficulty.
Hardcore difficulty: Successfully complete the game on the Hard difficulty.
Max Payne Advanced Character Model: Successfully complete the game on the Old School difficulty.
New York Minute mode in Arcade mode: Successfully complete the game on any difficulty.
Old School difficulty: Successfully complete the game on the Hard difficulty.
One Hit Kill cheat: Successfully complete the game on the Hardcore difficulty.
Unlimited Painkillers cheat: Successfully complete the game on the Hard difficulty.